Some ultra compact loudspeakers often include a passive radiator to extend the bass reproduction emitted from the loudspeakers. A passive radiator functions as a speaker without a motor (voice coil and magnet). A passive radiator generates an extra resonance and adds a complex pole pair to the transfer function of the loudspeaker, which results in a complex fifth order electromechanical model for the loudspeaker.
Identification of passive radiator parameters is essential for correct tuning and sound compensation of the loudspeaker. Such identification has previously been very complicated due to the complex pole pair resulting from the passive radiator. In some applications identification is performed using a special separate test box that requires a laser to measure the movement of the passive radiator in response to stimulus signals generated by an active sound source, such as an active speaker. These identification techniques and test boxes are very costly and time consuming to operate.